How do you divide the expression 3x^2 + 11x + 4 by x^4?

To divide the expression 3x² + 11x + 4 by x⁴, we start by reorganizing the division:

The expression can be rewritten in quotient form:

(3x² + 11x + 4) ÷ x⁴

Now, let’s break this down step by step:

1. Each term in the polynomial will be divided by x⁴.
2. We divide 3x² by x⁴:

3x² ÷ x⁴ = 3 ÷ x² = 3x^{-2}

3. Next, we divide 11x by x⁴:

11x ÷ x⁴ = 11 ÷ x³ = 11x^{-3}

4. Lastly, we divide 4 by x⁴:

4 ÷ x⁴ = 4x^{-4}

Combining all these results, we get:

3x^{-2} + 11x^{-3} + 4x^{-4}

This can also be expressed as a single fraction:

\frac{3}{x²} + \frac{11}{x³} + \frac{4}{x⁴}

Therefore, the final answer to dividing the expression 3x² + 11x + 4 by x⁴ is:

3x^{-2} + 11x^{-3} + 4x^{-4}